Resonance and stability of piezoelectric herringbone gears under time-delay feedback

This research presents a novel examination of vibrational properties and stability transformation dynamics in piezoelectric webbed herringbone gear systems subjected to delayed control mechanisms. These components play a vital role in the primary gearbox assemblies of rotary-wing aircraft. Our work develops a sophisticated nonlinear dynamical framework that integrates time-delayed feedback control for analyzing herringbone gear dynamics. Through application of the multi-timescale analytical approach, we systematically explore the amplitude-frequency behavior during fundamental resonance phenomena. Comprehensive numerical analyses, incorporating stability assessment protocols, further elucidate how temporal delay parameters influence system stabilization. The findings indicate that strategic configuration of positional gain coefficient g1 and damping gain coefficient g2 can substantially mitigate resonant oscillations, despite increased parameter sensitivity under elevated frequency conditions. Precise coordination of time delay variables td and tv enhances dynamic characteristics considerably, while improper synchronization may induce destabilization effects.